I guess they are not given a choice..they live and grow up in a strange land ..A land that does not belongs to their Father....but they have no choice to learn the culture to survive to fit in....and later in time they just forget their original identity...but I won say many have loose their identity..there are also ppl who has not forgotten their roots....
Do you think it depends which country you migrate to??? hmmm..Just a question ..
Actually, it's a natural process for overseas chinese to adapt to the culture of the country where he is born or grown up. There is actually a chinese idiom called "Ru Jin Sui Su 入境随俗" (entering a foreign place and adapt to the custom).
Usually, the 1st and 2nd generation immigrants will still retain their root culture, but the 3rd generation (those no longer born in China) will probably lose the language or cultural identity, if the family doesn't speak anymore chinese language. They are usually assimilated or integrated to the nationality or country where he belongs to. It really depends on the family.
To be honest, the chinese are probably more accustomed to retaining their root culture and language than other races/ethnicity. Usually, the german immigrants are completely assimilated in America. But the chinese tends to establish schools in order to maintain some link with their root language and culture.
In Singapore and Malaysia, chinese schools were founded that eventually allowed chinese language to be retained and take root making it one of the official languages in these countries. In Indonesia, there were also chinese schools, although over the past 20 years, there has been suppression of chinese language learning in Indonesia.
In the US, there are also some chinese language evening schools for kids to learn chinese. I've also been to a Taiwanese chinese school in the UK where kids continue to learn some chinese. It might be harder for those living in the west (esp. the 3rd generation) to retain their root culture, as the chinese are the minorities.